$$\left[\left(-\dfrac{2}{3}\right)^{-2}\right]^3\times \left(\dfrac{1}{3}\right)^{-4}\times 3^{-1}\times \dfrac{1}{6}$$
$$\left[\left(-\dfrac{3}{2}\right)^{2}\right]^3\times 3^{4}\times \dfrac{1}{3}\times \dfrac{1}{3\times 2}$$
$$\left(-\dfrac{3}{2}\right)^6\times (3)^2\times \dfrac{1}{2}$$
$$=\dfrac{3^{6+2}}{2^{6+1}}$$
$$=\dfrac{3^8}{2^7}$$